Another reason could be that Harry has a different view on creativity. He may think that only the original creators should be allowed to create stories within that universe. Fanfiction, which is created by fans, might seem to him like an infringement on the original work or just something that dilutes the purity of the original concept.
Well, Harry Potter has his own real and complex life. He has grown up in a difficult situation, facing challenges and traumas. Fanfiction is a concept from our world, outside of his own experiences. He's more concerned with the things that directly impact him, like the Triwizard Tournament, his relationship with Dumbledore, and the mystery of his parents' death. Fanfiction doesn't have a place in his immediate concerns. He's constantly in a battle against the forces of evil, and that takes up all his attention.
Because he lives in his own world. Fanfiction is something made by fans in our world, not in his magical world. He has no way to know about it.
Maybe it's out of guilt. In the original story, Danzo has done some shady things that might have affected Naruto indirectly. So in fanfiction, he could care about Naruto as a way to make amends.
He might be so immersed in his own real (in - story) life that fan - made stories seem unimportant. He has gods to deal with, monsters to fight, and friends to protect. Fanfiction is something created by fans outside of his own reality, so he has no reason to care.
Well, it could be that he doesn't care much about time travel in fanfiction. Harry is a character who is deeply rooted in his own time's problems. He's constantly facing challenges like the Triwizard Tournament, school exams, and the battle against the Dark Lord. Time travel might just add more complexity that he doesn't want to deal with. Also, his sense of loyalty is to his current friends and the wizarding world as it is, not some altered past or future through time travel.
Maybe it's a way to atone for something. Apollo might have done something in the past that affected Percy or his friends negatively, and by taking care of Percy, he is trying to make up for it. Or perhaps there is a prophecy that involves both of them, and Apollo taking care of Percy is part of fulfilling that prophecy.
They might show their care by protecting Harry from bullies at Hogwarts. In many fanfictions, Fred and George are known for their mischievous but kind - hearted nature. They could use their pranks to divert the attention of those who mean harm to Harry, or they might directly stand up to them when Harry is in trouble.
Maybe it's a way of stating that the integrity of the original Harry Potter character is not influenced by fanfic. Since fanfic can sometimes deviate greatly from the original source, saying 'harry potter doesn't care fanfic' is like saying the original character remains untouched by these fan - created ideas. Fanfic often has different interpretations of characters, and this statement could be a way to uphold the original view of Harry Potter.
In fanfiction, sometimes the writers have their own interpretations. They could see Naruto's character in a way where his goals and dreams, like becoming Hokage, are so all - consuming that he simply doesn't have the emotional space to care about Sakura. His attention is diverted to more important things in his mind, such as protecting the village and his friends in a more general sense rather than having a special care for Sakura.
Well, it could be that she simply doesn't have the time or inclination. Fanfiction often takes the characters in different and sometimes wild directions. Kishina, as a part of the original Naruto universe, might be more concerned with the integrity of the core story. And also, she might not be aware of the existence of fanfiction at all. After all, not everyone in the Naruto world is tuned into the fan - created content outside of their own story world.